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Cognitive radio (CR) has been considered as a promising technology to improve the spectrum utilization. In this paper we analyze the capacity of a CR network with average received interference power constraints. Under the assumptions of uniform node placements and a simple power control scheme, the maximum transmit power of a target CR transmitter is characterized by its cumulative distribution function (CDF). We study two CR scenarios for future applications. The first scenario is called the CR based central access network, which aims at providing broadband access to CR devices. In the second scenario, the so-called CR assisted virtual multiple-input multiple-output (MIMO) network, CR is used to improve the access capability of a cellular system. The uplink ergodic channel capacities of both scenarios are derived and analyzed with an emphasis on understanding the impact of numbers of primary users and CR users on the capacity. Numerical and simulation results suggest that the CR based central access network is more suitable for less-populated rural areas where a relatively low density of primary receivers is expected; while the CR assisted virtual MIMO network performs better in urban environments with a dense population of mobile CR users.